Ohio State University Algebraic Geometry SeminarYear 20182019Time: Tuesdays 34pmLocation: MW 154 

TIME  SPEAKER  TITLE 
August 21
Tue, 3pm  HsianHua Tseng
(OSU) 
The descendant Hilb/Sym correspondence for the plane 
September 4
Tue, 3pm  Rachel Webb
(Michigan) 
The AbelianNonabelian Correspondence for Quasimap Ifunctions 
October 2
Tue, 4:15pm  Ruth Charney
(Brandeis) 
Rado Lecture Series 2018 
October 9
Tue, 3pm  Angelica Cueto
(OSU) 
Anticanonical tropical del Pezzo cubic surfaces contain exactly 27 lines 
October 16
Tue, 3pm  Harry Richman
(U Michigan) 
Equidistribution of tropical Weierstrass points 
October 23
Tue, 3pm  Daniel Hast
(Rice) 
Rational points and unipotent fundamental groups 
October 30
Tue, 3pm  Pengyu Yang
(OSU) 
Rational points on homogeneous varieties 
November 6
Tue, 3pm  TBA
() 
TBA 
November 13
Tue, 3pm  TBA
() 
TBA 
November 20
Tue, 3pm  TBA
() 
TBA 
November 27
Tue, 3pm  Brooke Ullery
(Harvard) 
TBA 
December 4
Tue, 3pm  Brent Doran
(Oxford) 
TBA 
January 8
Tue, 3pm  TBA
() 
TBA 
January 15
Tue, 3pm  TBA
() 
TBA 
January 22
Tue, 3pm  Graham Denham
(Western Ontario) 
TBA 
January 29
Tue, 3pm  TBA
() 
TBA 
February 5
Tue, 3pm  TBA
() 
TBA 
February 12
Tue, 3pm  TBA
() 
TBA 
February 19
Tue, 3pm  TBA
() 
TBA 
February 26
Tue, 3pm  TBA
() 
TBA 
March 5
Tue, 3pm  TBA
() 
TBA 
March 7
Thurs, 4:15pm TBD  Valery Lunts
(Indiana) 
Colloquium 
March 12
Tue, 3pm  (break)


March 19
Tue, 3pm  TBA
() 
TBA 
March 2527
Tue, 4:10pm TBD  Pavel Etingof
(MIT) 
Zassenhaus Lecture Series 2019 
April 2
Tue, 3pm  TBA
() 
TBA 
April 9
Tue, 3pm  TBA
() 
TBA 
(Tseng): Let S be a nonsingular surface. A version of the crepant resolution conjecture predicts that the descendant GromovWitten theory of Hilb^{n}(S), the Hilbert scheme of n points on S, is equivalent to the descendant GromovWitten theory of Sym^{n}(S), the nfold symmetric product of S. In this talk we discuss how this works when S is C^{2}. We explicitly identify a symplectic transformation equating the two descendant GromovWitten theories. We also establish a relationship between this symplectic transformation and the FourierMukai transformation which identifies the (torusequivariant) Kgroups of Hilb^{n}(C^{2}) and Sym^{n}(C^{2}). This is based on joint work with R. Pandharipande.
(Webb): When a complex reductive group G with maximal torus T acts on an affine variety S, one can form two (GIT) quotients: W//G and W//T. With the right hypotheses, W//G and W//T are both smooth projective varieties. The relationship between the cohomology rings of these two varieties is well understood. I will discuss the relationship of their quantum cohomology using the quasimap theory of CiocanFontanine and Kim. In particular, I will present the abeliannonabelian correspondence for quasimap Ifunctions when W is a vector space and G is connected.
(Cueto): Since the beginning of tropical geometry, a persistent challenge has been to emulate tropical versions of classical results in algebraic geometry. The wellknow statement "any smooth surface of degree three in P^{3} contains exactly 27 lines'' is known to be false tropically. Work of Vigeland from 2007 provides examples of tropical cubic surfaces with infinitely many lines and gives a classification of tropical lines on general smooth tropical surfaces in TP^{3}. In this talk I will explain how to correct this pathology by viewing the surface as a del Pezzo cubic and considering its embedding in P^{44} via its anticanonical bundle. The combinatorics of the root system of type E_{6} and a tropical notion of convexity will play a central role in the construction. This is joint work in progress with Anand Deopurkar.
(Richman): The set of (higher) Weierstrass points on a curve of genus g > 1 is an analogue of the set of Ntorsion points on an elliptic curve. As N grows, the torsion points "distribute evenly" over a complex elliptic curve. This makes it natural to ask how Weierstrass points distribute, as the degree of the corresponding divisor grows. We will explore how Weierstrass points behave on tropical curves (i.e. finite metric graphs), and explain how their distribution can be described in terms of electrical networks. Knowledge of tropical curves will not be assumed, but knowledge of how to compute resistances (e.g. in series and parallel) will be useful.
(Hast): Given a curve of genus at least 2 over a number field, what can we say about its set of rational points? Faltings' theorem tells us that this set is finite, but many questions remain about how to obtain good bounds on the number of rational points and how to provably list all rational points. We will survey some recent progress and ongoing work on these questions using Kim's nonabelian Chabauty method, which uses the fundamental group to construct padic analytic functions that vanish on the set of rational points.
In particular, we present a new proof of Faltings' theorem for
superelliptic curves over Q, due to joint work with Jordan
Ellenberg. We will also discuss a conditional generalization of this
strategy from Qpoints to points in any real number field.
(Yang): Given a Fano variety X over a number field, and a height function on X. Manin's conjecture predicts the asymptotic growth of the number of rational points on X of bounded height. When X is an equivariant compactification of a homogeneous variety, the conjecture is related to equidistribution of adelic periods. We will discuss some recent progress in this direction.
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